Ascent spectrum and essential ascent spectrum

Tom 187 / 2008

O. Bel Hadj Fredj, M. Burgos, M. Oudghiri Studia Mathematica 187 (2008), 59-73 MSC: 47A53, 47A55. DOI: 10.4064/sm187-1-3

Streszczenie

We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space $X$ has finite dimension if and only if the essential ascent of every operator on $X$ is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator $F$ on $X$ has some finite rank power if and only if $\sigma_{{\rm asc}}^{{\rm e}} (T+F)=\sigma_{{\rm asc}}^{{\rm e}} (T)$ for every operator $T$ commuting with $F$. The quasi-nilpotent part, the analytic core and the single-valued extension property are also analyzed for operators with finite essential ascent.

Autorzy

  • O. Bel Hadj FredjUFR de Mathématiques, UMR-CNRS 8524
    Université de Lille 1
    59655 Villeneuve d'Ascq, France
    e-mail
  • M. BurgosDepartamento de Análisis Matemático
    Universidad de Granada
    18071 Granada, Spain
    e-mail
  • M. OudghiriFaculté des Sciences
    Université d'Oujda
    Oujda, Maroc
    e-mail

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